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incommensurable, a. (n.)|ɪnkəˈmɛnsjʊərəb(ə)l, -ʃər-|
[ad. med.L. incommensurābilis, also in Fr. (Oresme, 14th c.) which may be the intermediate source: see in-3 and commensurable.]
1. Math. Not commensurable; having no common measure (integral or fractional). Said of two or more quantities or magnitudes, or of one quantity or magnitude in relation to another (const. with, † to); also sometimes absol. = incommensurable with ordinary or ‘rational’ quantities, as the natural numbers; the same as irrational or surd (but not usually said, like these, of roots).
1570Billingsley Euclid x. def. ii. 229 Incommensurable magnitudes are such, which no one common measure doth measure. 1571Digges Pantom. iii. viii. R j b, These lines for that they are some of them incommensurable, can not exactly be expressed, saue only in surde numbers. a1688Cudworth Immut. Mor. (1731) 271 That the Diameter of every Square is Incommensurable with the Sides. 1710J. Clarke Rohault's Nat. Phil. (1729) I. 33 Suppose ABCD to be a Square, it may be geometrically demonstrated, that the Side AB, is incommensurable to the Diagonal AC. 1837–9Hallam Hist. Lit. I. i. iii. §136. 242 The rules as to surd roots are referable to incommensurable magnitudes. Mod. The ratio of the circumference of a circle to its diameter (denoted by π) is an incommensurable quantity.
b. (in Arith.): Having no (integral) common measure except unity; prime to one another.
1557Recorde Whetst. B j, If thei haue no suche common diuisor, then are thei called incommensurable, as 18 and 25. 1806Hutton Course Math. I. 53 If it happen that the common measure thus found is 1; then the numbers are said to be incommensurable, or not having any common measure.
2. gen. Having no common standard of measurement; not comparable in respect of magnitude or value.
1660R. Coke Justice Vind. 12 Whether such things so apprehended by the Senses, be pleasant, profitable, just or unjust..commensurable, or incommensurable. 1664H. More Myst. Iniq. Apol. 539 Will not this Position prove as incommensurable to humane affairs and be laden with as great inconveniences? 1796Burke Let. Noble Ld. Wks. 1842 II. 260 Between money and such services..there is no common principle of comparison: they are quantities incommensurable. 1845De Quincey Nat. Temperance Movem. Wks. XII. 167 The two states are incommensurable on any plan of direct comparison. 1881Westcott & Hort Grk. N.T. II. 46 The rival probabilities represented by relative number of attesting documents must be treated as incommensurable.
b. spec. Not worthy to be measured with; not coming up to the standard of measurement of (something); utterly disproportioned to.
1799–1805S. Turner Anglo-Sax. (1836) I. iii. iv. 188 The forces of either were so incommensurable with the numbers and bravery of the people they attacked. 1856Dove Logic Chr. Faith vi. §2. 340 His past life is incommensurable with infinity. 1892Stevenson & L. Osbourne Wrecker x. 173 Solutions, which I still dismissed as incommensurable with the facts.
B. n. An incommensurable quantity, etc.: usually in pl.
1741Watts Improv. Mind i. i. §3 Puzzling enquiries concerning..incommensurables. 1812Edin. Rev. XX. 94 Omitting to introduce any thing concerning the nature of incommensurables. 1845H. Rogers Ess. I. iii. 125 Melancthon was ‘cutting and contriving’ to perform impossibilities, to find a common measure of incommensurables. |